It was not known what path the ex-tropical cyclone would follow beyond Tuesday, Ms Flynn said.
"At this stage, the most likely scenario is that Ula will move south-eastwards, remaining well offshore of New Zealand. However, due to the uncertainty in the forecast track, MetService meteorologists will continue to monitor the movement of this system and, if necessary, severe weather watches and warnings will be issued."
In the deep south, Sunday had a blustery start. The highest gust was recorded early this morning at Mid Dome, in central Southland, where wind gusts reached 193km an hour. Mt Cook experienced gusts up to 118km/h, and Invercargill recorded 113km/h.
Air New Zealand spokeswoman Brigitte Ransom said no flights had been affected. No one from Jetstar could be contacted.
Winds had begun to ease as a ridge of high pressure moved on to the country, she said.
That high pressure would bring settled weather for many today and tomorrow, except in some eastern and central parts of the North Island and the Canterbury high country, where showers are expected.
Meanwhile, Oxfam warned today Cyclone Ula could deliver further heartache to those living in parts of Vanuatu devastated by last year's powerful Cyclone Pam.
Oxfam New Zealand spokeswoman Lucy Grogan said Ula was expected to pass close to islands in the Tafea province this afternoon, with wind speeds at its centre estimated to be up to 165km/h and possibly higher.
Oxfam was ready to help if needed, and donations could be made to its Disaster Response Fund, which responds to humanitarian crises worldwide. Donations can be made here.